I've had remarkable luck even where I don't have status- the Sheraton Seattle checked us in at 1 PM just last month, and hotels in Europe have been nice about letting me check in after an AM arrival on the redeye- but I never count on it. For early-morning arrivals in India I've reserved a room the night before and made it clear that I was coming in early that morning. That's worked very well with the exception of the Crowne Plaza in Gurgaon; I got in at 11 PM from the ORD-DEL nonstop and was offered free dinner (already stuffed from the plane) or the lounge. It took an hour till I had a room and I had to be in the office the next AM. I supect they charged someone taking a late-night flight extra to stay in "my" room while also charging me for that night, then didn't get it ready for me in time.

Disney hotels are absolutely inflexible. Doesn't matter if half their rooms are empty and cleaned, check-in time is the official posted time. One of the reasons I don't consider Disney World "The Happiest Place on Earth".